Finite Group Databasebeta

← Group #136553

Character table — Group #136553

Order 512.

C1C2C3C4C5C6C7C8C9C10C11C12C13C14C15C16C17C18C19C20C21C22C23C24C25C26C27C28C29C30C31C32C33C34C35C36C37C38C39C40C41C42C43C44C45C46C47C48C49C50C51C52C53C54C55C56C57C58C59C60C61C62
size111122222222222244444444444888888888888888888816161616161616161616161616163232
order12222244444488884448888888844448888888161616161616161644448888881616161644
χ111111111111111111111111111111111111111111111111111111111111111
χ211111111111111111111111111111111111111-1-1-1-1-1-1-1-1111111-1-1-1-1-1-1-1-1-1-1
χ311111111111111111111111111111111-1-1-1-11111111111-1-1-1-1-1-1-1-1-1-11111-1-1
χ411111111111111111111111111111111-1-1-1-111-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-1-1-111
χ5111111111111111111111-1-1-1-111-1-1-1-111111-1-111111111-1-1-1-1111111-1-1-1-1-1-1
χ6111111111111111111111-1-1-1-111-1-1-1-111111-1-1-1-1-1-1-1-1-1-1-1-1-1-111-1-1-1-1111111
χ7111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1111111111111-1-1-1-1-1-1-1-1-1-111
χ8111111111111111111111-1-1-1-111-1-1-1-11-1-1-1-1-1-1-1-1-1-1-1-1-1-11111-1-111111111-1-1
χ91111-1-1-1-111-1-111111-11-1-1ii−i−i-1-1ii−i−i1ii−i−ii−iiiii−i−i−i−i11-1-1i−i11-1-111-1-1i−i
χ101111-1-1-1-111-1-111111-11-1-1ii−i−i-1-1ii−i−i1ii−i−ii−i−i−i−i−iiiii11-1-1i−i-1-111-1-111−ii
χ111111-1-1-1-111-1-111111-11-1-1ii−i−i-1-1ii−i−i1−i−iiii−iiiii−i−i−i−i-1-111−ii-1-11111-1-1−ii
χ121111-1-1-1-111-1-111111-11-1-1ii−i−i-1-1ii−i−i1−i−iiii−i−i−i−i−iiiii-1-111−ii11-1-1-1-111i−i
χ131111-1-1-1-111-1-111111-11-1-1−i−iii-1-1−i−iii1ii−i−i−iiiiii−i−i−i−i-1-111i−i11-1-1-1-111−ii
χ141111-1-1-1-111-1-111111-11-1-1−i−iii-1-1−i−iii1ii−i−i−ii−i−i−i−iiiii-1-111i−i-1-11111-1-1i−i
χ151111-1-1-1-111-1-111111-11-1-1−i−iii-1-1−i−iii1−i−iii−iiiiii−i−i−i−i11-1-1−ii-1-111-1-111i−i
χ161111-1-1-1-111-1-111111-11-1-1−i−iii-1-1−i−iii1−i−iii−ii−i−i−i−iiiii11-1-1−ii11-1-111-1-1−ii
χ17222222222222-2-2-2-2222-2-22222-2-2-2-2-2-2-2000022000000000000000000000000
χ18222222222222-2-2-2-2222-2-2-2-2-2-2-2-22222-20000-2-2000000000000000000000000
χ19222222-2-222222222-2-2-2220000-2-20000-2222200000000000000-2-20000000000
χ20222222-2-222222222-2-2-2220000-2-20000-2-2-2-2-200000000000000220000000000
χ21222222-2-22222-2-2-2-2-2-2-2-2-200002200002000000000000002-22-2000000000000
χ22222222-2-22222-2-2-2-2-2-2-2-2-20000220000200000000000000-22-22000000000000
χ23222222-2-2-2-2-2-2000022-2002i2i−2i−2i00000000000−2i2i22−2−222−2−20000000000i2−i2i2−i200
χ24222222-2-2-2-2-2-2000022-2002i2i−2i−2i00000000000−2i2i−2−222−2−2220000000000−i2i2−i2i200
χ25222222-2-2-2-2-2-2000022-200−2i−2i2i2i000000000002i−2i22−2−222−2−20000000000−i2i2−i2i200
χ26222222-2-2-2-2-2-2000022-200−2i−2i2i2i000000000002i−2i−2−222−2−2220000000000i2−i2i2−i200
χ272222-2-22222-2-22222-22-2-2-20000220000-22i2i−2i−2i00000000000000−2i2i0000000000
χ282222-2-22222-2-22222-22-2-2-20000220000-2−2i−2i2i2i000000000000002i−2i0000000000
χ292222-2-22222-2-2-2-2-2-2-22-2220000-2-200002000000000000002-2-22000000000000
χ302222-2-22222-2-2-2-2-2-2-22-2220000-2-20000200000000000000-222-2000000000000
χ312222-2-222-2-22200002-2-200222200000000000-2-2i2i2−i2−i2−i2−i2i2i20000000000−i2i2i2−i200
χ322222-2-222-2-22200002-2-200222200000000000-2-2−i2−i2i2i2i2i2−i2−i20000000000i2−i2−i2i200
χ332222-2-222-2-22200002-2-200-2-2-2-20000000000022i2i2−i2−i2−i2−i2i2i20000000000i2−i2−i2i200
χ342222-2-222-2-22200002-2-200-2-2-2-20000000000022−i2−i2i2i2i2i2−i2−i20000000000−i2i2i2−i200
χ352222-2-2-2-222-2-2-2-2-2-22-22222i2i−2i−2i22−2i−2i2i2i-200002i−2i000000000000000000000000
χ362222-2-2-2-222-2-2-2-2-2-22-2222−2i−2i2i2i222i2i−2i−2i-20000−2i2i000000000000000000000000
χ3722-2-22-2002-22-222-2-20002-2000000000002-22-2002−22−22−22−20000002−22−2000000
χ3822-2-22-2002-22-222-2-20002-2000000000002-22-200−22−22−22−22000000−22−22000000
χ3922-2-22-2002-22-222-2-20002-200000000000-22-22002−22−22−22−2000000−22−22000000
χ4022-2-22-2002-22-222-2-20002-200000000000-22-2200−22−22−22−220000002−22−2000000
χ4122-2-2-22002-2-2222-2-2000-22000000000002i−2i−2i2i00i2−i2i2−i2−i2i2−i2i20000002−2−22000000
χ4222-2-2-22002-2-2222-2-2000-22000000000002i−2i−2i2i00−i2i2−i2i2i2−i2i2−i2000000−222−2000000
χ4322-2-2-22002-2-2222-2-2000-2200000000000−2i2i2i−2i00i2−i2i2−i2−i2i2−i2i2000000−222−2000000
χ4422-2-2-22002-2-2222-2-2000-2200000000000−2i2i2i−2i00−i2i2−i2i2i2−i2i2−i20000002−2−22000000
χ4544444444-4-4-4-40000-4-440000000000000000000000000000000000000000000
χ464444-4-4-4-4-4-4440000-4440000000000000000000000000000000000000000000
χ4744-4-44-4004-44-4-4-444000-4400000000000000000000000000000000000000000
χ4844-4-44-400-44-44000000000000000000000000002-2-222-2-220000000000000000
χ4944-4-44-400-44-4400000000000000000000000000-222-2-222-20000000000000000
χ5044-4-4-44004-4-44-4-4440004-400000000000000000000000000000000000000000
χ5144-4-4-4400-444-4000000000000000000000000002i−2i−2i2i−2i2i2i−2i0000000000000000
χ5244-4-4-4400-444-400000000000000000000000000−2i2i2i−2i2i−2i−2i2i0000000000000000
χ534-44-4004-400002i2−2i22i2−2i2000002i2−2i22i2−2i22i2−2i22-22-20000000000000000000000000000000
χ544-44-4004-400002i2−2i22i2−2i200000−2i22i2−2i22i22i2−2i2-22-220000000000000000000000000000000
χ554-44-4004-40000−2i22i2−2i22i2000002i2−2i22i2−2i2−2i22i2-22-220000000000000000000000000000000
χ564-44-4004-40000−2i22i2−2i22i200000−2i22i2−2i22i2−2i22i22-22-20000000000000000000000000000000
χ574-44-400-4400002i2−2i22i2−2i20000022−22−2222−2i22i2−2i2i2i−2i0000000000000000000000000000000
χ584-44-400-4400002i2−2i22i2−2i200000−222222−22−2i22i22i−2i−2i2i0000000000000000000000000000000
χ594-44-400-440000−2i22i2−2i22i20000022−22−22222i2−2i22i−2i−2i2i0000000000000000000000000000000
χ604-44-400-440000−2i22i2−2i22i200000−222222−222i2−2i2−2i2i2i−2i0000000000000000000000000000000
χ618-8-88000000004i2−4i2−4i24i20000000000000000000000000000000000000000000000
χ628-8-8800000000−4i24i24i2−4i20000000000000000000000000000000000000000000000

Here i is the imaginary unit (i² = −1).